Want to block a friend who is a bit too talkative on Facebook? You can effectively block a user completely, making it impossible for them to communicate with you. If blocking the person completely seems a bit harsh, you can turn off instant chat for specific users. Thus, you will appear to them to be offline.
Steps
Method 1 of 2: Block a user

Step 1. Click the Facebook menu button (▾)
It is located on the right side of the toolbar, at the top of the page.

Step 2. Select Settings from the menu

Step 3. Click on the Blocking option in the menu on the left of the settings page

Step 4. Enter the name of the user you want to block in the Block users field

Step 5. Click the Block button in the search results for the user you want to block

Step 6. Confirm that you want to block the user
- This action will block the user and prevent them from sending you messages.
- The user will no longer be able to see any content on your log. Blocking a user is an extreme action. Use this option only when you want to permanently end contact with a person.
Method 2 of 2: Disable instant chat for a user

Step 1. Click the Settings button at the bottom of the Facebook instant chat list
It looks like a gear.

Step 2. Select Advanced Settings from the menu

Step 3. Enter the name of the person for whom you want to turn off instant chat
As you type the name of the user, a list of people matching the search will appear, where you can select the user you are looking for.

Step 4. Click Save
It won't block the person, but any future messages they write to you will go straight to your inbox.